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On Confidence Bounds for the Bauer‐Köhne Two‐Stage Test
Author(s) -
Frick H.
Publication year - 2002
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/1521-4036(200203)44:2<241::aid-bimj241>3.0.co;2-r
Subject(s) - confidence interval , mathematics , combinatorics , statistics , upper and lower bounds , regular polygon , monotonic function , hazard ratio , distribution (mathematics) , cdf based nonparametric confidence interval , robust confidence intervals , tolerance interval , mathematical analysis , geometry
Bauer and Köhne (1994) described a two‐stage test for experiments with adaptive interim analysis. For distributions F ( x — θ), lower (1 — α)‐confidence bounds for θ are considered here which are consistent with this test. It turns out that all consistent bounds fall below the nominal level 1 — α for those F where log [1 — F ( x )] is strictly convex on an appropriate interval. A consistent bound C is given which maintains the (1 — α)‐confidence level for distributions with concave log [1 — F ], e.g. for the normal distribution and all distributions with monotonically non‐decreasing hazard rate. Generally it holds: if this C falls below the (1 — α)‐level for some F , then a consistent (1 — α)‐confidence bound for this F does not exist.